Best bakeries in Chelsea are more useful as a morning route than a ranking: start with one serious pastry, use Pavilion Road well, then decide whether King's Road deserves another stop.
Birley Bakery is the serious first-pastry stop; go early and decide what you want before the counter makes the decision for you.
Pavilion Road is the walking stretch between stops; there is no need to buy a second breakfast.
Chelsea beer gardens are better as a measured afternoon route: choose one proper outdoor destination, use King's Road only when it helps, and leave before the plan becomes a crawl.
Pick the garden for the afternoon you have, not because a pub owns some outdoor furniture.
The Phene and The Hollywood Arms are destinations; pavement tables are a different proposition entirely.
Things to do in Chelsea without wasting the day: Sloane Square, Pavilion Road, Saatchi Gallery, Chelsea Physic Garden, and a few places that justify the postcode.
Start around Sloane Square because it gives Chelsea structure without letting shopping take over.
Pavilion Road is the best low-effort introduction: coffee, bakeries, food shops, and enough village energy to soften the postcode.